In Section  we prove the exact-dimensionality of push-forward original and fibre Mandelbrot cascade measures, and that their dimension are the same. We first show in Theorem REF  the exact-dimensionality for the fibre cascade measures, following the method of Feng and Hu [1]}. Then we show in Theorem REF  that the original cascade measure is exact-dimensional and has the same dimension, following the arguments of Ledrappier and Young [2]}.
